Perhaps no one has more at stake in this year’s presidential election than the ultra-wealthy.

If Republican front-runner Mitt Romney reaches the White House, he will push for the top 1 percent of American earners to save an average of $150,000 in taxes, according to an analysis of his tax plan by the Tax Policy Center. In a second Obama administration, these Americans would pay about $83,000 more than they do now.

For the top 0.1 percent, the difference is even more stark. Romney’s plan would save them an average of $725,000. President Obama would raise their taxes by $450,000.

Romney and Obama’s tax proposals for the rich offer a window into how differently the two men understand the economy: what makes it tick, what the government can do to encourage wealth and how to rebuild the middle class.

Both men seek to assuage a growing anxiety among Americans about their economic security. But they use different language to describe the problem and offer different cures.

Obama has repeatedly called income inequality “the defining issue of our time.” He has proposed raising taxes on millionaires, saying on Tuesday that “broad-based prosperity has never trickled down from the success of a wealthy few.”

Romney, by contrast, waves off Obama’s talk of income inequality as the “politics of envy.” He says the best way to lift people out of poverty and raise wages is to help businesses become more successful. Ease regulations on businesses and lower taxes, Romney argues, and people’s fortunes will rise.

Neither candidate has a strong record of stemming a decades-long trend in this country of widening fortunes between the wealthiest Americans and everybody else.

Obama has overseen a recovery that has overwhelmingly benefited the wealthy. A recent study showed that the top 1 percent of Americans enjoyed 93 percent of the income gains from 2010, the first year of the recovery.

In Massachusetts, Romney did little to reverse the trend of income inequality that was happening in his state. And his work at Bain Capital embodied a pure distillation of American capitalism in which higher returns for investors, not worker pay, were the highest priority. If elected, Romney has pledged to curb deductions and other tax benefits for high-income households, but he has not been specific.

The Occupy Wall Street movement brought a new level of awareness to Americans of the growing income disparity between the richest 1 percent and the rest of the country. Obama is betting that a longer national conversation about inequality will help him win reelection. Romney, whose own income puts him in the upper reaches of “the 1 percent,” thinks that strategy will backfire.

“I think it’s fine to talk about those things in quiet rooms and discussions about tax policy and the like,” Romney said in January on “The Today Show.” “But the president has made it part of his campaign rally. It’s a very envy-oriented, attack-oriented approach, and I think it will fail.”

Romney’s record

When Romney was governor of Massachusetts from 2003 to 2007, his state, like many others, was experiencing growing inequality between top and bottom earners.

Massachusetts was still reeling from the bursting of the tech bubble. It was also in the midst of a decades-long bleeding of manufacturing jobs. Under Romney, manufacturing payroll employment dropped more than 14 percent, giving the state the third-worst record nationally during that time, according to analysis by Andrew Sum, director of the Center for Labor Market Studies at Northeastern University.

Average weekly wages for workers rose slightly more than they did nationally while Romney was in charge. In Massachusetts, wages went up 4.1 percent from 2002 to 2006, adjusting for inflation. Nationally, they rose 3.2 percent.

But those gains were not spread evenly. Those who worked in investment banking and securities trading saw their average weekly wages rise 60 percent, from $2,707 in 2002 to $4,852 in 2006, according to census data adjusted for inflation.

Sum says the loss of manufacturing jobs helped exacerbate income inequality by making it tougher for blue-collar workers to find employment.

The trend continued after Romney left.

“I don’t think there’s any evidence to suggest he made it worse,” said Michael D. Goodman, associate professor and chairman of the Department of Public Policy at the University of Massachusetts at Dartmouth. “This is a long-term phenomenon that continued under his watch. He’s not the only governor who’s presided over this trend.”

Romney frequently touts his work at Bain Capital as evidence that he knows how to lower the country’s unemployment. Yet many of the jobs he cites as having helped to create have salaries that would be unlikely to pay enough to support a middle-class family.

Their relatively low pay highlights how hard it can be to generate jobs that pay well enough to close the income gap.

His campaign says Romney helped create 100,000 jobs while at Bain, including 15,000 at the Sports Authority and 89,000 at Staples.

There are no public data on the average pay for a Sports Authority or Staples employee, but data from the Bureau of Labor Statistics offer some hints.

According to government data, the median hourly wage at “sporting goods stores” such as Sports Authority is $10.44 an hour; the average annual salary is $26,470.

These figures fall short of the median household income in the United States in 2010, which was $49,455.

Obama’s record

Obama is seeking to address some of these issues by raising taxes on millionaires to ensure that they pay at least 30 percent. The White House has not divulged details on how the tax increase would be structured.

The president would also allow Bush-era tax cuts for those making more than $250,000 to expire. By contrast, Romney would make the Bush tax cuts permanent for everyone and cut individual income tax rates by an additional 20 percent.

“It’s no surprise Romney doesn’t want to talk about the middle class,” said Kara Carscaden, deputy national press secretary for Obama’s reelection campaign. “Romney opposes the Buffett Rule that makes sure millionaires and billionaires don’t pay lower tax rates than the middle class, and he opposes eliminating tax loopholes that benefit Wall Street. That’s a clear contrast with President Obama, who believes we need to reward hard work and responsibility.”

But as much as Obama has been pushing to raise taxes on the wealthy, he has also presided over a recovery in which the rich have done far better than the poor.

During the recession, from 2007 to 2009, the share of income earned by the top 1 percent of American workers stayed flat. As the stock market crashed, both high-wage and low-wage earners saw their incomes drop.

But the recovery has been much tougher for those on the lower end.

In 2010, the top 1 percent of Americans on average saw their incomes rise 11.6 percent, according to a recent study by Emmanuel Saez, an economist at the University of California at Berkeley. By contrast, the rest of the country inched up 0.2 percent. In other words, writes Saez, “the top 1% captured 93% of the income gains in the first year of recovery.”

A primary driver of inequality has also been exploding executive pay. Although the White House vowed to rein in compensation at companies that benefited the most from taxpayer-paid bailouts, some large salaries were still approved. The administration’s “pay czar,” for instance, approved a $10.5 million pay package for the chief executive of American International Group.

Courting the middle class

Both Obama and Romney have been targeting middle-class Americans for support. In fact, Romney has been so eager to prove his bona fides with these voters that in February he said he was, by contrast, “not concerned about the very poor.”

“The best thing we can do for the economic well-being of the people of America is not to grow government; it is to restore freedom and opportunity,” Romney said. “To build a strong economy that provides good jobs and rising wages and that reduces poverty, we need to build successful businesses of every kind imaginable.”

Obama’s view is that income inequality itself creates a broader economic problem that is bad for everyone.

“What drags down our entire economy is when there’s an ever-widening chasm between the ultra-rich and everybody else,” Obama said last week.

Given the myriad causes of income inequality, there are questions about whether tweaking the tax code, as Obama has suggested, is a sufficient solution.

“Using the tax code to address that issue is almost like treating a symptom and not treating the disease,” said Howard Gleckman, a resident fellow at the Urban Institute and editor of the Tax Policy Center’s blog, TaxVox. But, he adds, giving further tax benefits to the rich could exacerbate things.

“It’s not even a problem of, ‘Do you want to use the tax code to smooth out some of the inequality?’” Gleckman said. “The question is: Do you actually want to reform the code in ways that make that inequality worse?”

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